Question

For a constant volume batch reactor, solve for the temporal concentration profiles, e.g. CA(t) and CB(t) at each initial condition (IC) Given) Reversible elementary reaction kA (forward) A B ka (backward) dCkCkC dt dCkC-kC, dt k 0.0001s) k0.00005(s 1 IC at t-0, CAO= 0.5 (mol/dm) and CBo 0 (mol/dm IC at t-0, CAO 0.5 (mol/dm') and CBo 0.2 (mol/dm 2. Using any ODE solver, solve the coupled ODEs for two initial conditions Need to submit graphs (CA and CB vs t at each IC) with the title of your name and also its code. If you did not use Matlab, also need to mention about the software name.

Answer 1

By using matlab,

for IC 1, we get

C_A(t) =

21t 10e20000 1 -+ 42 21 -

C_B(t) =

21 10e 20000 10 21 21

for IC 2 we get,

C_A(t) =

-21t 1 e 20000 15 30

C_B(t) =

21t 2 E 20000 3 15

The output images are shown below

IC 1 0.5 0.45 0.4 Cr Ca 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 0 1000 2000 3000 4000 6000 7000 8000 5000 9000 10000

IC 2 0.7 0.6 Ca Cr 0.5 0.4 0.3 0.2 0.1 0 1000 2000 3000 4000 5000 6000 7000 8000 9000

The code is

syms A(t) B(t)
>> ode1= diff(A)==0.00005*B-0.001*A;
>> ode2= diff(B)==0.001*A-0.00005*B;
>> odes(t)=[ode1,ode2];
>> odes(t)=[ode1;ode2];
>> cond1= A(0)==0.5;
>> cond2= B(0)==0;
>> cond3 = A(0)== 0.5;
>> cond4= B(0)==0.2;
>> conds=[cond1;cond2];
>> [usol(t),vsol(t)]=dsolve(odes,conds)

usol(t) =

(10*exp(-(21*t)/20000))/21 + 1/42


vsol(t) =

10/21 - (10*exp(-(21*t)/20000))/21

>> conds1=[cond3;cond4];
>> [Asol(t),Bsol(t)]=dsolve(odes,conds1)

Asol(t) =

(7*exp(-(21*t)/20000))/15 + 1/30


Bsol(t) =

2/3 - (7*exp(-(21*t)/20000))/15